Critical Path Method Explained with Cookies

The Critical Path Method (CPM) is a scheduling technique that demonstrates the time periods for which it’s possible to perform a project activity. This is accomplished through calculating for each activity the early start, late start, early finish, and late finish. Individual activities also have float, which is the amount of flexible time for the activity to occur without delaying the overall schedule. CPM is a technique of the fourth edition PMBOK®’s Develop Schedule process.

Here is an example. Katy is going to bake a batch of cookies. She tells her son that he needs to have the table set by the time the cookies are done so the family can sit down together and eat the cookies. There are two paths through the network—baking cookies and setting the table. Baking cookies includes three activities: mixing dough (takes 5 minutes); putting the cookies onto the baking sheet (takes 10 minutes); and baking the cookies (takes 20 minutes). Setting the table has two activities: washing the table (takes 2 minutes) and setting the table (takes 5 minutes). After these two activities, the family will spend 10 minutes eating the cookies.

Katy’s son doesn’t want to stop playing before he has to, so he makes a network diagram. First he must do the forward pass.

1. He places “0” in the Early Start boxes (top left corner) for the two starting activities—Mix Dough and Wash Table.
2. He places the duration of each activity in the Duration boxes (top middle). So for Mix Dough, he places “5” representing 5 minutes, for Cookies on Sheet he places “10”, etc.
3. He calculates the Early Finish for each activity by first adding the Early Start and Duration boxes for the starting activities. So for Mix Dough, he adds “0” and “5” and places “5” in the Early Finish box. That “5” in the Early Finish box is then moved forward and also put in the Early Start box for the next activity, which is Cookies on Sheet. The Early Finish for the Cookies on Sheet activity is calculated by adding this “5” to the Cookies on Sheet duration (which is “10”) and that equals “15”. He finishes calculating all the Early Finish times for all activities. Note that for Eat Cookies, the Early Start is “35” because it is the larger of the two preceding tasks’ Early Finishes (Bake Cookies has “35” and Set Table has “7” for their Early Finishes).

Now that he has completed the forward pass, with the end calculation of finishing eating the cookies after 45 minutes of beginning the process, it is time for the backward pass.

1. That “45” Early Finish for the Eat Cookies activity is also placed as the Late Finish (bottom right corner) for Eat Cookies.
2. He calculates the Late Start (bottom left corner) by subtracting the Duration from the Late Finish. So the Late Start for Eat Cookies is the Late Finish of “45” minus the Duration of “10” which is “35”.
3. The Float is calculated by subtracting the Early Finish from the Late Finish. Also, the Early Start can be subtracted from the Late Start…the result is the same. So for the Eat Cookies activity, the Float can be calculated either as “35” minus “35” or as “45” minus “45”. Either way, the resulting Float is “0” and that is placed in the bottom middle box.
4. The Late Finish for Bake Cookies and Set Table is the same as the Late Start for Eat Cookies which is “35”. (Note: if there were another task also dependent on Bake Cookies and Set Table being complete before it could start, whichever later task had the smaller Late Start time would be the Late Finish for Bake Cookies and Set Table.
5. The remaining Late Start, Float, and Late Finish times can now be filled in.

The baking cookies path takes longer than the setting the table path in terms of minutes to complete, so it is the critical path. Katy’s son examines the Late Start for Wash Table, and now he knows that when his mother starts baking cookies, he has no more than 28 minutes of playtime before he has to start washing and then setting the table, or he will be in trouble!